For Windows, you just need to extract the new version of the game into an empty folder. For Android, you need to update the game without uninstalling it.
In detail, the save files can be found in the following directory depending on your operating system:
Windows: %APPDATA%/RenPy/TownOfMagic
Example: C:\Users\[USER]\AppData\Roaming\RenPy\TownOfMagic
MacOS: library/RenPy/TownOfMagic/
Linux: ~/.renpy/TownOfMagic
Android: Phone\Android\data\www.townofmagic.com\files\saves
If a save loading does not work, try loading a save from the Q section of the loading screen.